Numerical Modeling of the Three‐Dimensional Unsteady Convection of a Silicon Melt in a Vessel Typical of Czochralski‐Method Apparatuses

Calculations of the quasiperiodic and stochastic regimes of threedimensional convection of a silicon melt (Pr = 0.015) have been performed for a rotating vessel whose complicated shape is typical of crucibles used in growing crystals by the Czochralski method. A large set of data on the structure of the convection and the spectral composition of pulsations has been obtained. The influence of the rotation of a crystal and a crucible on the convection and the thermal state of a melt has been investigated.     

Some Three‐Dimensional Effects of Heat and Mass Transfer in a Fire within a Building

Results of a numerical investigation of heat and mass transfer at the initial stage of a fire within a building in combustion of a liquid fire load, performed with the use of a threedimensional mathematical field model, are presented. Formulas approximating the calculation results are proposed for estimation of the maximum time of operation of an opening to release the gas from the building and determination of the size of the zone within which a change in the position of the fire load causes no marked changes in the parameter of heat and mass transfer. Threedimensional inhomogeneities in the temperature and velocity fields, which have a profound impact on the problems of providing fire safety for buildings, are revealed.     

Generalized Equations of One‐Dimensional Filtration with Fractional‐Power Differentiations

Based on the formalism of fractionalpower integrodifferentiation, the theory of filtration in porous media with fractal structure is generalized. Consideration is given to the cases of steady and unsteady filtration. For the steady filtration, nonlinear solutions are shown to exist. In the unsteady case, a new class of periodic solutions may exist.     

Thermal Conductivity of a Molecular Crystal with Rotational Degrees of Freedom: Orientational Defect Scattering

Measurements of thermal conductivity of solid methane-deuteromethane solutions at equilibrium vapor pressure in the temperature range 1.2÷20 K are reported. The obtained dependences of thermal conductivity on temperature and concentration can be explained qualitatively assuming that the dominant mechanism of phonon scattering is connected with the interaction of phonons with the rotational motion of the molecules in all of the three orientational phases of the CH₄-CD₄ system. The contribution of the orientational defect scattering to the thermal conductivity is discussed in frame of the model of local changes in the moments of inertia of molecules.      

Two‐Dimensional Diffusion of a Binary Mixture of Neutral Gases

An expression for the coefficient of twodimensional diffusion of a binary mixture of neutral gases is obtained within the framework of the kinetic theory.     

Two‐Dimensional Stationary Temperature Field of a System of Bounded Inhomogeneous Cylinders which Are in Ideal Thermal Contact

The problem on uniform stationary lateral heating of two bounded cylindrical bodies with different thermophysical characteristics which are in ideal thermal contact within the region of contact has been considered. The exact analytical solution of this problem has been obtained and the conditions of energy balance have been investigated.     

Diagnosis of the Thermal Bow of a Shaft in a Three Stage Centrifugal Compressor

In practice many turbo-machines driven by motors are started up to perational speed within a very short time,i.e.in less than 20 seconds .For this type of machines the compatibility of thermal deformaiton of the rotor stucture must be taken into account in the machine desing ,or the thermal defromation will be constrained and a huge resultant force can cause the shaft bending and consequently resulting in violent vibrations.In this paper,detection of thermal bow of a shaft in a three stage centrifugal compressor in a petrochemical plant is presented .The diagnostic results show that the thermal bow was induced by the incompatibility of axial thermal deformation of the rotor stucure.A remedial action allowing free axial thermal expansion of the outer parts of the rotor is suggested.     

Thermal Conductivity and Thermal Diffusivity of Liquid Indium–Tin Alloys

Thermal-conductivity and thermal-diffusivity coefficients of indium–tin alloys have been determined using the laser flash method over the temperature range from the liquidus line to 1173 K. Measurements were performed using the setup LFA-427 of NETZSCH company in an argon protective atmosphere, and cells were produced from molybdenum. The equations for temperature dependences of the thermal conductivity and thermal diffusivity of In–Sn alloys have been obtained. The results of measurements were compared with data available in the literature.     

Thermal Conductivity and Thermal Diffusivity of Pulse-Heated W–Re Alloys

Results are reported for the thermal conductivity and thermal diffusivity as a function of temperature for four W–Re alloys (4.0, 21.24, 24.07, and 31.09 mass% of Re) over a wide temperature range covering the solid and liquid states. The measurements allow the determination of specific heat and dependences among electrical resistivity, temperature, and density of the alloys into the liquid phase. The thermal conductivity is calculated using the Wiedeman–Franz law. Additionally, data for thermal conductivity and thermal diffusivity of the constituent elements, tungsten and rhenium, are presented for the first time. Both metals have been previously studied with the same experimental technique.     

Mathematical Model of a Recuperative Heat Exchanger in a Two‐Dimensional Formulation

A twodimensional model of a recuperative heat exchanger which allows calculation of flows through a heattransfer wall and temperature at any point of it has been developed. The results of the calculations are in satisfactory agreement with experimental data.     

Thermal Gravitational‐Capillary Convection in a Cavity with a Longitudinal Temperature Gradient

Convective heat exchange in a flow of liquid in a rectangular cavity with the lengthtoheight ratio of a liquid layer L/H = 10 is investigated. The conditions of thermal insulation or linear distribution of temperature were kept on the lower horizontal surface. Three types of boundary conditions for velocity were set on the upper boundary: rigid, free without friction, and free with imposition of a thermocapillary effect. The vertical walls of the cavity are isothermal and heated to different temperatures. The investigated regimes were of thermogravitational, thermocapillary, and thermal gravitationalcapillary convection. A comparative analysis of the evolution of flow structure with increase in the Rayleigh (Ra) and Marangoni (Ma) numbers is carried out.     

Heat Transfer in Straight Channels with Two‐Dimensional Cross‐Sectional Profiles under Conditions of Nonisothermal Stabilized Flow of a Fluid

Heat transfer in stabilized regimes of nonisothermal flows in a round tube and in channels with twodimensional convex cross sections is investigated with allowance for the velocity profile of a heating or cooling flow of a fluid. Mathematical models of unsteady processes of cooling by convection and radiation in pulling of rods and plane sheets at a constant velocity and of heat transfer (mass transfer) in a thin runningdown layer of a medium (fluid) are solved.     

Two‐Dimensional Calculation of the Parameters of a Steam‐Air Mixture in a Film‐Type Heat and Mass Exchanger

A mathematical model for twodimensional calculation of the temperature and density of the steam in a steamair mixture which rises between two water films flowing down adiabatic shields has been proposed. The parameters of the films have been calculated in a onedimensional approximation. The results of calculating the parameters of air according to the onedimensional and twodimensional models of the processes of heat and mass transfer have been compared. The range of applicability of the former to a filmtype heat and mass exchanger has been determined.     

Investigation of Thermal Processes in Gas‐Thermal Spraying of Metal‐Ceramic Coatings

The features of the thermal regime of gasthermal deposition of metalceramic coatings have been studied. The procedure of calculation of the temperature field of a multicomponent coating throughout the process of formation has been developed. The quantitative dependences of the character of heating of the deposited particles and melting of the substrate on the thermophysical properties and chemical composition of the material, the intensity of heat exchange, and the technological parameters of the process have been established. The thermal conditions of spraying of powder compositions, which ensure improved strength characteristics of the coating–substrate system, have been determined.     

Thermal Calculation of the Furnace Chamber of a Fire‐Tube Boiler With a Dead‐End Furnace

An engineering procedure for calculating the thermal regime of the furnace chambers of firetube boilers with a deadend furnace is given. The procedure proposed is devoid of many drawbacks that are inherent in the standard method for calculating boiler units and permits more accurate allowance for the special features of combined energy exchange in furnace chambers of boilers that differ significantly in type and size from traditional ones.     

Solution of Nonlinear Two‐Dimensional Differential Equations of Transfer with Discontinuity Boundary Conditions on the Surface of an Isotropic Semiinfinite Body in Its Heating Through a Circle of Known Radius

An analytical solution of the heatconduction problem is obtained by the method of linearization of a nonlinear equation of transfer and combined application of integral transforms to the linearized problem for an isotropic halfspace heated through a circular region 0 < r < R on its surface z = 0.     

One Approach to the Analytical Solution of a Two‐Dimensional Nonstationary Problem of Heat Conduction in Regions with Moving Boundaries on the Model of a Half‐Space

With the use of the solution of the Dirichlet nonstationary problem with discontinuous unmixed boundary conditions on the surface of an isotropic halfspace a twodimensional model of the problem with a moving phase boundary is considered. The problem models, for example, the processes of freezing of moist ground or the processes of formation of ice in stagnant water if a temperature lower than the freezing temperature is prescribed on the boundary surface in a circular region of finite radius. The classical onedimensional result follows as a particular case from solution of this problem for an infinite radius of the circle.     

The Nonaxisymmetric Contact Thermoelastic Problem for a Half‐Space with a Motionless Rigid Spherical Inclusion

Based on the generalized Fourier method used simultaneously in the spherical and cylindrical systems of coordinates, we suggested an analytical method for solving the contact problem of thermoelasticity for an elastic halfspace with a rigid spherical inclusion. The problem is reduced to an infinite system of linear algebraic equations with the Fredholm operator provided that the boundary surfaces do not intersect. An approximate solution of the system in the form of a series with respect to a small parameter is obtained. The numerical analysis of the problem is presented.     

Calculation of the Nonstationary, Nonlinear Three‐Dimensional Problem of Heat Conduction by the Finite‐Element Method in Continuous Laser Heating

The process of nonstationary highintensity laser surface heating of a threedimensional body in the shape of a rectangular parallelepiped by a continuous laser with a normal distribution of the power density in the heating spot has been investigated numerically with the finiteelement method. Consideration has been given to the process of formation of the heataffected zone and its geometry. Thermal cycles of zonal points and their characteristics have been investigated.     

Thermal Conductivity of Cobalt-Based Catalyst for Fischer–Tropsch Synthesis

In this study, the thermal conductivity of cobalt-based catalyst specimens in the temperature range from 160 ^◦C to 255 ^◦C are measured via a steady-state apparatus. The apparatus and procedures are applied to several specimens of cobalt-based catalyst powder compacts. Specimens with different degrees of porosity are produced by pressing cobalt-based catalyst powder with a particle size of (80 to 360) mesh. The thermal conductivity of cobalt-based catalyst powder compacts is investigated as functions of temperature, specimen density, porosity, and powder size. The results indicate that the thermal conductivity of the catalyst specimens increases linearly with temperature and density and is practically independent of the particle size of the powder in an atmosphere of air, while the porosity dependence of the thermal conductivity is inverse to that of density. In addition, the effects of some measuring factors on the thermal conductivity show that the reliability of the thermal conductivity measurements of cobalt-based catalyst specimens are influenced easily by parallelism, specimen roughness, and moisture content, whereas the specimen thickness and water bath temperature have only a slight effect on the reliability.